Question

pt 6 of 10 (10 complete) x 11.5.69 Suppose p = 400 - Vg2 + 10 is a demand equation for a manufacturer's product. (a) Find the rate of change of p with respect to q. (b) Find the relative rate of change of p with respect to q. (c) Find the marginal-revenue function.

Answer 1

Ans: p = 400 - Vq² Ho a) Rate of change of f with respect to a ple-400 - q²t10 Differentiating both sides with respect to a p(q) = dp x &q da dq 2dq tio Ja etio Rate at which a changes with respect to 2: Negative sign indicates there is an inverse relationship between p and a 6) Relative rate of change of p with respect to a It is given by ratio of function to function R(q)) = Relative rate of change of p with respect toq R(p(q)) = _ p'q dp/dq derivation P (9) Je to Dividing 0 and ③ p(q) -4 0-Jq²t10 2 - 400-5q²tio pla Vq²tio q'to po yoo - Jqz tio q 400 sq² +10 (22+10) (1q++10) P.TO

dom 400g #lo - 13410 pla 400 q²+10 •q ²-10 - Relative rate of change of p with respect to p(q) 2 TR= p. q total c) Marginal revenue is the rate of change of revenue (TR) with respect to 2 Total Revenue = p. q Putting value of p = Yoo-Jq² tio TR (400-dq²+1a). q TR = 400 g - (Jq² +10). q TR = 400 q - qq +10 TR with respect to q & applying Multiplicature 400 da Differentiating MR = d(TR) = q? +10 2 MR = (TR) 400 q² tło da +10 MR you?"+r) -2-01+) 2710 MR = 400 89² +10) - q - q² - 1 Jq' tio MR = 400 (892 +10) 292-10 1 q²tio

MR = 400 gatot Qq2H0) (wq²Ho) q²t10 400- 292 +10) Marginal ✓q²+10 Revenue function MR =